Optimal Policies for the Inventory Problem with Negotiable Leadtime

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Abstract
In this paper we study the dynamic inventory problem in which amounts of stock ordered at unit prices ck and ck+1 (ck > ck+1) are delivered, respectively, k and k + 1 periods later. It is demonstrated that under suitable cost conditions, the optimal policies are similar to those of the dynamic inventory problem with a delivery lag of k + 1 periods, except for an additional constant stock level up to which it is desired to order at unit price cK. If we assume that ordering decisions are made in every other period, it is demonstrated that analogous results are obtainable for the case in which amounts of stock ordered at unit prices ck, ck+1, and ck+2 (ck > ck+1 > ck+2) are delivered, respectively, k, k + 1, and k + 2 periods later.

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